相关论文: Exploiting Aggregate Sparsity in Second Order Cone…

This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex…

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…

Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…

This paper proposes a sequential convex relaxation method for obtaining feasible and near-globally optimal solutions for unit commitment (UC) with AC transmission constraints. First, we develop a second-order cone programming (SOCP)…

Two-dimensional (2D) fully-addressed arrays can conveniently realize three-dimensional (3D) ultrasound imaging while fully controlled such arrays usually demands thousands of independent channels, which is costly. Sparse array technique…

The LP-Newton method solves the linear programming problem (LP) by repeatedly projecting a current point onto a certain relevant polytope. In this paper, we extend the algorithmic framework of the LP-Newton method to the second-order cone…

Machine learning (ML) approaches are increasingly being used to accelerate combinatorial optimization (CO) problems. We investigate the Set Cover Problem (SCP) and propose Graph-SCP, a graph neural network method that augments existing…

One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…

This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…

Sparse codes in neuroscience have been suggested to offer certain computational advantages over other neural representations of sensory data. To explore this viewpoint, a sparse code is used to represent natural images in an optimal control…

In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the…

Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma, Ahmed and Nemhauser (2008) and Hijazi, Bonami and…

The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…

Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…

Traditional largest normalize residual (LNR) test for bad data identification relies on state estimation residuals and thus can only be implemented after running Power System State Estimation (PSSE). LNR may fail to detect bad data in…

In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…